Summary

This project seeks to improve on the Howard et al. (2020) methods used to estimate sport fish harvest, catches and releases of rockfish in Alaska waters. This is essentially a Bayesian version of the Howard methods that allows for more appropriate and defensible sharing of information between areas, handles missing data in a more appropriate manor, accurately propagates uncertainty throughout the estimation procedure and thus does not rely on the decision tree approach in the original Howard methods. Furthermore, the Bayesian approach should provide sport fish harvest, catch and mortality estimates back to 1978 when the SWHS was implemented. Harvest estimates should be mostly consistent with Howard estimates during contemporary times, but may differ based on more appropriate weighting of SWHS and logbook data, including estimating and correcting bias in the SWHS data. Furthermore, the Howard methods are wholly reliant on logbook release estimates and ignore the release estimates from the SWHS data (inferred from the catch and harvest estimates). Here we explore several models that attempt to balance all of the data in estimating releases.

Data

Harvest data was available for 22 commercial fishing management areas in Southcentral and Southeast Alaska. Areas with negligible rockfish harvest were pooled with adjacent areas for analysis. Specifically the Aleutian and Bering areas were pooled into an area labeled BSAI; the IBS and EKYT were pooled into an area labeled EKYKT; the Southeast, Southwest, SAKPEN and Chignik areas were pooled into an area labeled SOKO2PEN and the Westside and Mainland areas were pooled into an area labeled WKMA.

Stateside Harvest Survey (SWHS)

Statewide harvest survey estimates of rockfish catch and harvest are available for 28 years (1996-2023) for all users and for 13 years (2011-2023) for guided anglers (Figure 0). Additionally, there are estimates from 1977- 1995 that required some partitioning work to ascribe to current management units. Harvests in unknown areas were apportioned based on harvest proportions in 1996. Variance estimates are not available for pre-1996 data and as such, the maximum observed coefficient of variation (cv) in each commercial fisheries management unit was applied.

**Figure 0.**- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.

Figure 0.- Data sources for estimating rockfish harvests and releases in ADF&G commercial fisheries management units.


SWHS estimates are believed to be biased to some degree. These modelling efforts aim to estimate and correct for that bias with the assumption that logbook harvests are a census of guided harvests.

Rockfish release estimates are inferred from the difference between catch and harvest estimates.

Adam noted that the first 5 years (23 years counting the historical data) in the SWHS data set for PWSO seem unreasonable (close to zero and not corroborated with logbook estimates). Adam recommended setting these harvests to unknown, but current model development has included the data. Once a satisfactory model has been identified we will exam the effects of censoring the PWSO data.

Creel Surveys

NA

Guide Logbooks

Sport fishing guides were required to report their harvest of rockfish for 26 years (1998-2023). Reported harvest is also available by assemblage (pelagic vs. non-pelagic). Harvest of yelloweye and “other” (non-pelagic, non-yelloweye) rockfish were reported separately beginning in 2006.

Logbooks also record the number of rockfish released for the same categories. However, the reliability of the release data is somewhat questionable as reported releases are generally far lower than that estimated by the SWHS. As such several treatments of the data are considered.

Logbook versus SWHS estimates

Estimates of guided harvests and releases from the SWHS do not align with the census from charter logbooks. Logbook harvest reports are generally considered reliable and are used to assess the bias in SWHS reports. However, there is even greater disparity between release estimates in the two sources and it is debatable whether logbook releases should be treated as a census. The Howard et al. (2020) methods do treat the logbook release data as “true” and thus are considerably less than would be estimated from the SWHS data.

**Figure 1.**- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).

Figure 1.- SWHS harvest estimates from guided trips (Hhat) versus repoted harvests from charter logbooks (H_lb).


The Howard methods treat the logbook release data as a census and then use the ratio of guided:unguided releases in the SWHS to expand the logbook release estimates to generate total and unguided estimates.

To evaluate this discrepancy, several models were used to estimate releases in this exploration. One method (\(LB_{fit}\)) considers the logbook release data to be reliable and a second method (\(LB_{cens}\)) treats the logbook release data as estimates of the minimum released, thus giving more weight to SWHS release estimates. A third method (\(LB_{hyb}\)) is a hybrid approach that treats reported releases of yelloweye as reliable but total rockfish and pelagic rockfish releases as minimums. Model development to date has revealed a tension between the total and pelagic logbook releases and the yelloweye logbook releases.

Composition data

Harvest sampling data exists from Gulf of Alaska areas since 1996 and from Southeast Alaska areas since 2006. Port sampling data is comprised of the number of total rockfish, pelagic and non-pelagic rockfish, black rockfish and yelloweye rockfish.

A current challenge at this juncture is how to accommodate the prohibition on retaining yelloweye in Southeast from 2020 through 2024. Because it is closed to retention the port sampling data is not reflective of releases while remaining an accurate description of the harvest. Current modelling efforts revolve around developing a separate yelloweye curve that censors the missing data.

Process equations

The true harvest \(H_{ay}\) of rockfish for area \(a\) during year \(y\) is assumed to follow a temporal trend defined by a penalized spline:

\[\begin{equation} \textrm{log}(H_{ay})~\sim~\textrm{Normal}(f(a,y), {\sigma_H}) \end{equation}\]

where \(f(a,y)\) in a p-spline basis with 7 components (knots) and a second degree penalty. The variance, \(\sigma_H\), was given a normal prior with a mean and standard deviation of 0.25 and 1, respectively.

Charter and private harvest \(H_{ayu}\) (where u = 1 for charter anglers and u = 2 for private anglers) is a fraction of total annual harvest in each area:

\[\begin{equation} H_{ay1}~=~H_{ay}P_{(user)ay1}\\H_{ay2}~=~H_{ay}(1-P_{(user)ay1}) \end{equation}\]

where \(P_{(user)ay1}\) is the fraction of the annual harvest in each area taken by charter anglers. \(P_{(user)ay1}\) was modeled hierarchically across years as:

\[\begin{equation} P_{(user)ay1}~\sim~\textrm{beta}(\lambda1_a, \lambda2_a) \end{equation}\]

with non-informative priors on both parameters.

Annual black rockfish harvest \(H_{(black)ayu}\) for each area and user group is:

\[\begin{equation} H_{(black)ayu}~=~H_{ayu}P_{(pelagic)ayu}P_{(black|pelagic)ayu} \end{equation}\]

where \(P_{(pelagic)ayu}\) is the fraction of the annual harvest for each area and user group that was pelagic rockfish and \(P_{(black|pelagic)ayu}\) is the fraction of the annual harvest of pelagic rockfish for each area and user group that was black rockfish.

The southeast region also tracks two other non-pelagic rockfish assemblages, demersal shelf rockfish (DSR, which includes yelloweye) and slope rockfish. For the southeast region the harvest of those two assemblages is thus

\[\begin{equation} H_{(DSR)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(DSR|non-pelagic)ayu}\\ H_{(slope)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(slope|non-pelagic)ayu}\\ \end{equation}\]

where \(P_{(DSR|non-pelagic)ayu}\) and \(P_{(slope|non-pelagic)ayu}\) are the fractions of the annual harvest of non-pelagic rockfish for each area and user group that were DSR and slope rockfish, respectively.

Annual yelloweye rockfish harvest \(H_{(yelloweye)ayu}\) for each area and user group is calculated differently for central/Kodiak areas and southeast areas. For central and Kodiak areas yelloweye rockfish harvests are calculated as

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{ayu}(1-P_{(pelagic)ayu})P_{(yelloweye|non-pelagic)ayu} \end{equation}\]

where \(P_{(yellow|non-pelagic)ayu}\) is the fraction of the annual harvest of non-pelagic rockfish for each area and user group that was yelloweye rockfish.

For southeast areas yelloweye harvests are a fraction of the DSR harvests such that

\[\begin{equation} H_{(yelloweye)ayu}~=~H_{(DSR)ayu}P_{(yelloweye|DSR)ayu} \end{equation}\]

The composition parameters \(P_{(comp)ayu}\), were modeled using a logistic curve that would allow hindcasting without extrapolating beyond the limit of observed values such that:

\[\begin{equation} \textrm{logit}(P_{(comp)ayu})~=~\beta1_{(comp)ayu} + \frac{\beta2_{(comp)ayu}}{(1 + exp(\beta3_{(comp)ayu}*(y - \beta4_{(comp)ayu})))} + \beta5_{(comp)ayu}*I(u=private)+re_{(comp)ayu} \end{equation}\]

where the \(\beta\) parameters define the intercept, scaling factor, slope, inflection point and private angler effect, respectively, \(y\) is the year index, \(I(u=private)\) is an index variable which is 1 when the user groups is private and 0 otherwise and \(re_{(comp)ayu}\) is a random effect with a non-informative prior.

The true number of released rockfish \(R_{ayu}\) were based on the proportion of the total catch harvested by area, year, user group and species grouping , \(pH_{(comp)ayu}\). Thus, converting \(H_{(comp)ayu}\) to total catches by user group, \(C_{(comp)ayu}\), with \(pH_{(comp)ayu}\) results in estimates of total releases such that

\[\begin{equation} R_{(comp)ayu}~=~ C_{(comp)ayu} - H_{(comp)ayu} ~=~ \frac{H_{(comp)ayu}}{pH_{(comp)ayu}} - H_{(comp)ayu} \end{equation}\]

with total releases equal to the sum of the compositional releases.

The proportion harvest parameters for \(pH_{(comp)ayu}\) were modeled using a logistic curve that would allow hindcasting based on trends in the data without extrapolating beyond the range of observed values such that

\[\begin{equation} \textrm{logit}(pH_{(pH)ayuc})~=~\beta1_{(pH)ayu} + \frac{\beta2_{(pH)ayuc}}{(1 + exp(\beta3_{(pH)ayuc}*(y - \beta4_{(pH)ayuc})))} + \beta5_{(pH)ayuc}*I(u=private)+re_{(pH)ayuc} \end{equation}\]

A random effect term allowed estimation during the historical period when data is available, but the curve defined by the above equation determined release estimates between 1977 and 1990.

Observation equations

SWHS estimates of annual rockfish harvest \(\widehat{SWHS}_H{ay}\) were assumed to index true harvest:

\[\begin{equation} \widehat{SWHS}_H{ay}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay}b_{ay}), \sigma_{SWHSHay}^2\right) \end{equation}\]

where bias in the SWHS harvest estimates \(b_H{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_H{ay}~\sim~\textrm{Normal}(\mu_H{(b)a}, \sigma_H{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

SWHS estimates of guided angler harvest \(\widehat{SWHS}_H{ay1}\) are related to total harvest by:

\[\begin{equation} \widehat{SWHS}_H{ay1}~\sim~\textrm{LogNormal}\left(\textrm{log}(H_{ay1}b_{ay}), \sigma_{SWHS_{ay1}}^2\right) \end{equation}\]

Reported guide logbook harvest \(\widehat{LB}_H{ay}\) is related to true harvest as:

\[\begin{equation} \widehat{LB}_H{ay}~\sim~\textrm{Poisson}(H_{ay1})\\ \widehat{LB}_H{(pelagic)ay}~\sim~\textrm{Poisson}(H_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_H{(yelloweye)ay}~\sim~\textrm{Poisson}(H_{(yelloweye)ay1})\\ \widehat{LB}_H{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(H_{(nonpel,nonye)ay1})\\ \end{equation}\]

Note that for central and Kodiak areas \(H_{(nonpel,nonye)ay1}\) is equal to the total harvest minus pelagic and yelloweye harvests. For southeast areas \(H_{(nonpel,nonye)ay1}\) is equal to the sum of the DSR and slope harvests minus yelloweye harvests.

SWHS estimates of annual rockfish releases \(\widehat{SWHS}_R{ay}\) were assumed to index true releases in a similar fashion and thus modeled similarly. Because logbook release data is more questionable and demonstrates greater disagreement with SWHS estimates (Figure 1), several approaches have been explored. In the first approach model \(LB_{fit}\) treats the release data as a true census and the releases are related to true releases just as harvests were modeled such that:

\[\begin{equation} \widehat{LB}_R{ay}~\sim~\textrm{Poisson}(R_{ay1})\\ \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{Poisson}(R_{ay1}P_{(pelagic)ay1})\\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

Similar to how harvests were modeled, central and Kodiak \(R_{(nonpel,nonye)ay1}\) was equal to total releases minus pelagic and yelloweye releases while for southeast areas it was equal to the sum of DSR and slope releases minues yelloweye releases.

In the second approach we consider the logbook release data to be a minimal estimate of the true releases. Thus model \(LB_{cens}\) censors the release data (censored data is entered as NA) and treats the reported releases as a minimal number such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(ye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(ye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(ye)ay}, \infty\right)\\ \text{censored} \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(nonpel,nonye)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(nonpel,nonye)ay}, \infty\right) \end{equation}\]

Model \(LB_{hyb}\) is a hybrid approach that treats the yelloweye releases as a reliable census of yelloweye releases (given the emphasis and ease of recording these fish) but censors the pelagic and total rockfish release estimates such that

\[\begin{equation} \text{censored} \widehat{LB}_R{ay}~\sim~\textrm{LogNormal}\left(\log(R_{ay}), 1\right)\text{T}\left(\widehat{LB}_R{ay}, \infty\right) \\ \text{censored} \widehat{LB}_R{(pelagic)ay}~\sim~\textrm{LogNormal}\left(\log(R_{(pelagic)ay}), 1\right)\text{T}\left(\widehat{LB}_R{(pelagic)ay}, \infty\right) \\ \widehat{LB}_R{(yelloweye)ay}~\sim~\textrm{Poisson}(R_{(yelloweye)ay1})\\ \widehat{LB}_R{(nonpel,nonye)ay}~\sim~\textrm{Poisson}(R_{(nonpel,nonye)ay1})\\ \end{equation}\]

SWHS estimates of guided angler release \(\widehat{SWHS}_R{ay1}\) is modeled the same as harvests.

SWHS release bias was modeled differently in the \(LB_{fit}\), \(LB_{cens}\), and \(LB_{hyb}\) models. Because the \(LB_{fit}\) model assumes that logbook release data is true and the poison likelihoods assume a much smaller variance than the large variances associated with the SWHS release estimates, SWHS release estimates \(b_R{ay}\) were modeled independently of the harvest bias \(b_H{ay}\) such that

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

where bias in the SWHS release estimates \(b_R{ay}\) is modeled hierarchically across years as:

\[\begin{equation} b_R{ay}~\sim~\textrm{Normal}(\mu_R{(b)a}, \sigma_R{(b)a}) \end{equation}\]

with non-informative priors on both parameters.

The \(LB_{cens}\) model treats the logbook release data as lower bound on the release estimates and thus the likelihood linking true releases to the SWHS release estimates is dominant. During model development it was apparent that estimating bias in the SWHS data was more difficult and a different structure was employed that assumed bias in SWHS release data followed a similar pattern to that of the harvests but is offset by some area specific amount. In these models \(b_R{ay}\) differed from \(b_H{ay}\) by offset \(Rboff_{a}\) such that

\[\begin{equation} b_R{ay}~=~b_H{ay} + Rboff_{ay} \end{equation}\]

where

\[\begin{equation} Rboff_{a}~\sim~\textrm{Normal}(\mu_{(bR)r}, \sigma_{(bR)r}) \end{equation}\]

such that \(Rboff_{a}\) was modeled hierarchically across region r.

The number of pelagic rockfish sampled in harvest sampling programs \(x_{(pelagic)ayu}\) follow a binomial distribution:

\[\begin{equation} x_{(pelagic)ayu}~\sim~\textrm{Binomial}(P_{(pelagic)ayu}, N_{ayu}) \end{equation}\]

where \(N_{ayu}\) is the total number of rockfish sampled in area \(a\) during year \(y\) form user group \(u\). The number of black rockfish sampled in harvest sampling programs and the number of yellow rockfish sampled modeled analogously with an appropriately substituted \(N\).

Unresolved issues and outstanding questions:

Models detailed in this markdown represent the next step in the modelling process whereby the pH parameters are separated out by species. This approach separates the compositional data that is germaine to the harvests from the release estimates and releases are now based on pH. Additionally, this approach allows the pH parameters to differ between pelagic and yelloweye which is appropriate given regulatory changes as well as fisherman and industry behaviour and is born out in the results. The approach results in great uncertainty around unguided release estimates, but that uncertainty is appropriate given the data. These models handle the yelloweye closures in southeast much more appropriately given that the compositional data is no longer directly applied to the release estimates. These versions of the model are in development and it is unclear whether the \(LB_{cens}\) model would work, but it appears applicable to the \(LB_{fit}\) and \(LB_{hyb}\) approaches.

Other issues include:

  1. Complete convergence has not been achieved and the logistic curve parameters for p_pelagic and p_yellow remain the last sticking point. I think that p_pelagic will resolve with longer chains.
  2. Estimate precision: These models are producing more precise harvest estimates that in Adam’s original model. I am not sure why at this juncture. sigma_H on the spline was switched from a fixed value to a prior centered around that fixed value, but the model estimates are in the same range as the fixed value. Would the number of knots in the spline explain this? 7 knots was settled on during early model fitting when it clearly performed better than fewer or more knots.
  3. Prior choices in general need to be vetted. The priors on the logistic curves are fairly informed in an effort to achieve the desired shapes for hindcasting. Ideally, sensitivity testing would occur but the model is very slow to converge. The beta parameters on the logistic curves have required a lot of work on the priors to reach convergence.
  4. Random effects on pH: These are currently used in the model but because pH isn’t linked to data as the p_comp data is I am not sure what to make of them or if they are appropriate.
  5. Model comparisons: I need to write code for comparing models side by side as well as quantifying the differences between these methods and the Howard methods.

Results

**Figure X.**- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Figure X.- Rhat values and proportion of parameters that converged (Rhat < 1.1.)

Estimate comparison

Since previous estimates of rockfish harvest have been produced these first 3 graphs will be used to show how the modeled estimates compare to the estimates produced earlier. For total rockfish the estimates are in general agreement although differences are noted. These estimates should be more reliable because they include both SWHS and guide logbook data, handle variance more appropriately, use hierarchical distributions when data is missing, directly consider observation error and are produced using reproducible research.

**Figure 2.**- Total rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 2.- Total rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 3.**- Total rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 3.- Total rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


Notes from Adam: When looking at only black rockfish the most significant differences are for the Prince William Sound Inside area. I did not spend a great deal of time tracking this down although it looks like the previous version used bad values for \(P_{(black)ayu}\) for at least unguided anglers. For the moment I would ignore the results for BSIA and SOKO2SAP. I think it is possible to give approximate values for these areas but it will require a little more coding which I have yet to do.

**Figure 4.**- Black rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 4.- Black rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.


And black rockfish releases…

**Figure 5.**- Black rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 5.- Black rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Yellow rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Yellow rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Yellow rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Yellow rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- DSR rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- DSR rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- DSR rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- DSR rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 6.**- Slope rockfish harvests 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 6.- Slope rockfish harvests 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.



**Figure 7.**- Slope rockfish releases 1996--2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Figure 7.- Slope rockfish releases 1996–2023. Lines and error polygons represent model estimates and points and error bars represent Howard et al estimates.

Model fit

Logbook residuals

**Figure 8.**- Residuals from logbook harvests

Figure 8.- Residuals from logbook harvests


SWHS residuals

**Figure 9.**- Residuals from SWHS harvests.

Figure 9.- Residuals from SWHS harvests.



**Figure 10.**- Residual of SWHS releases

Figure 10.- Residual of SWHS releases

Parameter estimates

P(Charter)

These histograms show the posterior distribution of the mean percent of rockfish harvested by the charter fleet.

**Figure 11.**- Mean percent of harvest by charter anglers.

Figure 11.- Mean percent of harvest by charter anglers.


When considered annually we see the percent of rockfish harvested by the charter fleet follows our data fairly well although we just do not have much information about this ratio. Prior to 2011 the percent charter is confounded with SWHS bias and should be mostly discounted.

**Figure 12.**- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

Figure 12.- Annual estimates of the percent of harvest by charter anglers for 16 commerical fishing manamgent areas, 1996-2023.

P(Harvest)

These plots show the fitted logistic line to the proportion of caught rockfish that are harvested. These estimates are used for hindcasting catch estimates based on the harvest data in early years when catch estimates are unavailable.


**Figure 13.**- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of pelagic rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.

Figure 13.- Annual proportion of yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available.


**Figure 13.**- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.

Figure 13.- Annual proportion of non-pelagic, non-yelloweye rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note, that this is not estimated for Southeast areas because non=pelagics are divided between DSR (including yelloweye) and Slope species.


**Figure 13.**- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of DSR rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.


**Figure 13.**- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

Figure 13.- Annual proportion of Slope rockfish catch that was harvested. Note that pre-1990 estimates are used to estimate catch in these years when catch estimates are not available. Note that the observed logbook data is for all non-pelagic, non-yelloweye fish.

SWHS bias

Figure 14 shows the mean estimate for SWHS bias. Cook Inlet, North Gulf Coast and North Southeast Inside all look pretty good while most other areas have substantial bias. Prince William Sound Inside has the largest bias.

**Figure 14.**- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 14.- Mean SWHS bias for harvests and catches. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.


Our estimates of SWHS bias track observations fairly well when he have guided harvest estimates. There are some disturbing trends/patterns seen in the earlier time periods. Often the patterns represent periods where SWHS estimates and guide logbook estimates do not follow the recent relationship. I’m not sure what drives the trends but it seems plausible to me that long-term changes in the ratio of charter and private anglers may be a factor. If Charter/Private ratio information is available in the historical creel data it my be helpful here (particularly for North Southeast Inside and South Southeast outside).

**Figure 15.**- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS *underestimates* the true value and bias > 1 indicates the survey *overestimates* the true value.

Figure 15.- Annual estimates of SWHS bias in harvests and releases for 16 commerical fishing manamgent areas, 1996-2023. Note that a bias < 1 indicates that the SWHS underestimates the true value and bias > 1 indicates the survey overestimates the true value.

P(pelagic)

We model the percentage of pelagic rockfish in the harvest because we have the information for charter anglers (via logbooks) starting in 1998. Other than looking at the model estimates you can use Figure 8 to compare the two data streams for pelagic rockfish harvest. In general they are in agreement with major exceptions in Price William Sound inside, Prince William Sound outside (early in the time series) and South Southeast inside.

**Figure 16.**- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 16.- Annual estimates of the percent of the sport harvest that was pelagic rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(black|pelagic)

Note that in Southeast Alaska we only have composition data starting in 2006. Tania dug up old SE data, but it did not provide any useful data for species apportionment.

**Figure 17.**- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

Figure 17.- Annual estimates of the percent of the sport harvest of pelagic rockfish that were black rockfish for 16 commerical fishing manamgent areas, 1996-2023.

P(yelloweye|non-pelagic / yelloweye|DSR)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were yelloweye rockfish for 16 commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

P(DSR|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were DSR rockfish for 6 Southeast commerical fishing manamgent areas, 1996-2023.

P(slope|non-pelagic)

**Figure 18.**- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.

Figure 18.- Annual estimates of the percent of the sport harvest of non-pelagic rockfish that were slope rockfish for 6 southeast commerical fishing manamgent areas, 1996-2023. Note that P(yelloweye) is the the proportion relative to non-pelagics for Central and Kodiak areas but is relative to DSR for Southeast areas.



Summary of unconverged parameters:

Table 1. Summary of unconverged parameters including the number (n) and the average Rhat from the unconverged parameters.
parameter n badRhat_avg
beta3_yellow 3 3.842192
mu_beta0_pH 2 2.711899
beta0_yellow 4 2.297567
beta0_pH 20 2.256857
beta3_pH 15 2.178049
beta3_black 3 1.597534
beta1_black 14 1.498979
mu_beta0_yellow 1 1.463776
beta2_pH 23 1.430206
beta1_pH 27 1.395787
beta0_black 5 1.393264
parameter n badRhat_avg
beta0_pelagic 3 1.345144
beta1_pelagic 7 1.345102
beta2_yellow 7 1.342254
beta2_black 7 1.338559
beta2_pelagic 6 1.304977
tau_beta0_pelagic 1 1.293180
beta1_yellow 5 1.270036
beta3_pelagic 2 1.238035
tau_beta0_yellow 2 1.188028
beta_H 1 1.186486
tau_beta0_pH 5 1.184613
Table 2. Summary of unconverged parameters by area
afognak BSAI CI CSEO eastside EWYKT NG northeast NSEI NSEO PWSI PWSO SOKO2SAP SSEI SSEO WKMA
beta_H 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 1
beta0_black 0 0 1 1 0 0 1 0 0 1 0 1 0 0 0 0
beta0_pelagic 0 0 0 0 1 0 1 0 0 0 1 0 0 0 0 0
beta0_pH 0 0 0 1 0 1 0 0 1 1 0 0 1 1 1 1
beta0_yellow 0 0 0 1 0 0 1 0 0 1 0 0 0 0 0 1
beta1_black 1 1 1 1 1 1 1 1 0 1 1 1 1 0 1 1
beta1_pelagic 1 0 0 0 0 0 1 1 1 0 1 0 1 0 0 1
beta1_pH 1 1 1 1 0 1 1 0 1 1 1 1 1 1 1 1
beta1_yellow 0 0 0 1 1 0 1 0 0 1 0 0 0 0 0 1
beta2_black 0 0 1 1 0 1 1 1 0 0 1 1 0 0 0 0
beta2_pelagic 0 0 0 0 1 0 0 0 0 1 1 1 1 0 0 1
beta2_pH 1 1 1 1 1 1 0 1 1 1 1 1 1 1 1 1
beta2_yellow 0 0 0 1 0 0 0 1 0 1 0 1 0 1 1 1
beta3_black 0 0 1 0 0 1 0 0 0 0 0 1 0 0 0 0
beta3_pelagic 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 1
beta3_pH 0 0 0 1 0 1 0 0 1 1 0 0 0 1 1 1
beta3_yellow 0 0 0 1 0 0 0 0 0 1 0 0 0 0 0 1
mu_beta0_pH 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
mu_beta0_yellow 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0
tau_beta0_pelagic 0 0 1 0 0 0 0 0 0 0 0 0 0 0 0 0
tau_beta0_pH 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0
tau_beta0_yellow 0 0 0 0 0 0 1 0 0 0 1 0 0 0 0 0

Parameter estimates:

Summary Table of Parameter Estimates
Parameter mean sd Lower_CI Median Upper_CI
mu_bc_H[1] -0.131 0.069 -0.257 -0.134 0.014
mu_bc_H[2] -0.098 0.044 -0.174 -0.102 -0.001
mu_bc_H[3] -0.433 0.071 -0.567 -0.435 -0.287
mu_bc_H[4] -0.989 0.196 -1.365 -0.987 -0.611
mu_bc_H[5] 0.898 0.968 -0.154 0.712 3.066
mu_bc_H[6] -2.194 0.329 -2.839 -2.200 -1.521
mu_bc_H[7] -0.475 0.114 -0.715 -0.468 -0.264
mu_bc_H[8] 0.247 0.362 -0.353 0.210 1.079
mu_bc_H[9] -0.302 0.134 -0.565 -0.302 -0.038
mu_bc_H[10] -0.119 0.067 -0.250 -0.122 0.018
mu_bc_H[11] -0.105 0.041 -0.183 -0.106 -0.021
mu_bc_H[12] -0.261 0.107 -0.486 -0.255 -0.059
mu_bc_H[13] -0.122 0.079 -0.270 -0.125 0.035
mu_bc_H[14] -0.274 0.094 -0.463 -0.270 -0.100
mu_bc_H[15] -0.342 0.054 -0.445 -0.341 -0.233
mu_bc_H[16] -0.210 0.401 -0.902 -0.243 0.658
mu_bc_R[1] 1.347 0.142 1.069 1.346 1.627
mu_bc_R[2] 1.492 0.089 1.317 1.492 1.663
mu_bc_R[3] 1.429 0.133 1.158 1.430 1.681
mu_bc_R[4] 0.990 0.195 0.576 1.000 1.342
mu_bc_R[5] 1.158 0.457 0.234 1.161 2.019
mu_bc_R[6] -1.543 0.429 -2.397 -1.543 -0.717
mu_bc_R[7] 0.298 0.190 -0.083 0.298 0.661
mu_bc_R[8] 0.540 0.201 0.136 0.542 0.926
mu_bc_R[9] 0.380 0.199 -0.054 0.400 0.722
mu_bc_R[10] 1.319 0.129 1.058 1.325 1.558
mu_bc_R[11] 1.123 0.075 0.983 1.122 1.270
mu_bc_R[12] 0.901 0.192 0.534 0.895 1.271
mu_bc_R[13] 1.056 0.101 0.863 1.056 1.257
mu_bc_R[14] 0.964 0.143 0.687 0.962 1.249
mu_bc_R[15] 0.885 0.095 0.697 0.886 1.069
mu_bc_R[16] 1.178 0.121 0.946 1.176 1.426
tau_pH[1] 2.800 0.273 2.301 2.791 3.373
tau_pH[2] 2.738 0.351 2.122 2.715 3.495
tau_pH[3] 2.878 0.420 2.114 2.851 3.737
tau_pH[4] 31.584 473.834 4.862 7.929 88.904
tau_pH[5] 4.277 2.443 1.065 4.255 9.152
beta0_pH[1,1] 0.519 0.232 0.036 0.527 0.948
beta0_pH[2,1] 1.306 0.256 0.732 1.318 1.766
beta0_pH[3,1] 1.349 0.244 0.845 1.361 1.799
beta0_pH[4,1] 1.617 0.257 1.048 1.629 2.098
beta0_pH[5,1] -0.526 0.420 -1.306 -0.543 0.433
beta0_pH[6,1] 0.138 0.583 -0.986 0.136 1.047
beta0_pH[7,1] 0.351 0.554 -0.794 0.592 1.024
beta0_pH[8,1] -0.513 0.317 -1.249 -0.472 -0.027
beta0_pH[9,1] -0.472 0.292 -1.061 -0.465 0.087
beta0_pH[10,1] 0.351 0.235 -0.076 0.340 0.832
beta0_pH[11,1] -0.243 0.251 -0.778 -0.220 0.204
beta0_pH[12,1] 0.486 0.262 -0.068 0.489 0.986
beta0_pH[13,1] -0.016 0.340 -0.640 -0.050 0.674
beta0_pH[14,1] -0.423 0.285 -1.020 -0.415 0.091
beta0_pH[15,1] -0.257 0.608 -1.179 -0.305 1.268
beta0_pH[16,1] 0.179 1.424 -1.904 -0.425 2.487
beta0_pH[1,2] 2.624 0.236 2.132 2.649 3.016
beta0_pH[2,2] 2.865 0.235 2.285 2.899 3.229
beta0_pH[3,2] 2.395 0.269 1.819 2.416 2.859
beta0_pH[4,2] 2.529 0.336 1.758 2.627 2.992
beta0_pH[5,2] 4.607 1.569 2.510 4.298 8.615
beta0_pH[6,2] 2.859 0.280 2.297 2.872 3.356
beta0_pH[7,2] 1.881 0.201 1.451 1.898 2.227
beta0_pH[8,2] 2.773 0.302 2.260 2.808 3.126
beta0_pH[9,2] 2.889 0.614 1.570 3.085 3.694
beta0_pH[10,2] 3.660 0.248 3.040 3.687 4.061
beta0_pH[11,2] -4.992 0.276 -5.508 -5.001 -4.468
beta0_pH[12,2] -4.954 0.449 -5.903 -4.936 -4.153
beta0_pH[13,2] -4.772 0.407 -5.609 -4.762 -4.005
beta0_pH[14,2] -5.653 0.464 -6.651 -5.626 -4.812
beta0_pH[15,2] -4.226 0.357 -4.955 -4.215 -3.545
beta0_pH[16,2] -4.900 0.356 -5.589 -4.904 -4.198
beta0_pH[1,3] 1.318 0.268 0.712 1.340 1.764
beta0_pH[2,3] 1.938 0.369 1.035 2.015 2.427
beta0_pH[3,3] 2.138 0.382 1.314 2.195 2.722
beta0_pH[4,3] 2.471 0.532 1.269 2.659 3.138
beta0_pH[5,3] 1.235 2.394 -4.017 1.186 6.186
beta0_pH[6,3] -0.882 1.551 -2.527 -1.427 3.164
beta0_pH[7,3] -1.979 0.808 -3.579 -1.973 -0.020
beta0_pH[8,3] 0.300 0.177 -0.049 0.300 0.645
beta0_pH[9,3] -0.046 0.333 -0.715 -0.055 0.600
beta0_pH[10,3] 0.784 0.301 0.062 0.810 1.314
beta0_pH[11,4] 0.417 1.889 -2.403 0.194 3.182
beta0_pH[12,4] 0.263 2.064 -2.550 0.016 3.069
beta0_pH[13,4] -0.063 2.539 -3.099 -0.839 4.178
beta0_pH[14,4] 0.172 1.881 -2.771 -0.125 3.113
beta0_pH[15,4] 0.517 2.113 -2.745 -0.082 4.149
beta0_pH[16,4] 0.308 2.069 -2.610 -0.385 3.799
beta0_pH[11,5] -0.763 0.297 -1.369 -0.749 -0.182
beta0_pH[12,5] -2.130 0.742 -3.205 -2.323 -0.550
beta0_pH[13,5] -0.525 0.676 -1.764 -0.529 0.698
beta0_pH[14,5] -0.964 0.280 -1.568 -0.940 -0.467
beta0_pH[15,5] -1.050 0.305 -1.577 -1.077 -0.213
beta0_pH[16,5] -0.784 0.330 -1.691 -0.732 -0.268
beta1_pH[1,1] 3.129 0.391 2.422 3.100 3.952
beta1_pH[2,1] 2.507 0.504 1.724 2.441 3.678
beta1_pH[3,1] 2.604 0.514 1.804 2.533 3.847
beta1_pH[4,1] 3.068 0.582 2.225 2.962 4.521
beta1_pH[5,1] 2.038 0.485 1.227 2.003 2.992
beta1_pH[6,1] 2.562 0.836 1.312 2.413 4.609
beta1_pH[7,1] 2.060 0.896 0.639 2.018 3.778
beta1_pH[8,1] 3.109 0.748 2.060 2.968 5.187
beta1_pH[9,1] 2.065 0.363 1.376 2.054 2.798
beta1_pH[10,1] 2.239 0.349 1.580 2.233 2.966
beta1_pH[11,1] 6.542 0.771 5.348 6.450 8.453
beta1_pH[12,1] 2.896 0.321 2.279 2.901 3.536
beta1_pH[13,1] 5.922 1.333 4.123 5.566 9.016
beta1_pH[14,1] 14.849 4.386 9.200 13.759 25.747
beta1_pH[15,1] 9.305 2.392 5.459 9.060 13.942
beta1_pH[16,1] 12.634 3.301 7.778 12.557 19.630
beta1_pH[1,2] 3.058 8.035 0.006 1.005 23.981
beta1_pH[2,2] 3.599 7.589 0.011 1.125 29.401
beta1_pH[3,2] 1.253 0.319 0.673 1.238 1.884
beta1_pH[4,2] 2.830 5.474 0.010 0.960 21.740
beta1_pH[5,2] 3.265 17.279 0.000 0.194 21.011
beta1_pH[6,2] 0.892 0.953 0.000 0.805 2.820
beta1_pH[7,2] 0.470 0.938 0.000 0.083 2.440
beta1_pH[8,2] 0.642 1.735 0.000 0.077 4.292
beta1_pH[9,2] 0.843 1.420 0.000 0.530 2.598
beta1_pH[10,2] 2.229 4.105 0.000 0.776 14.898
beta1_pH[11,2] 6.928 0.316 6.334 6.942 7.504
beta1_pH[12,2] 6.943 0.591 5.912 6.895 8.226
beta1_pH[13,2] 7.293 0.451 6.479 7.281 8.216
beta1_pH[14,2] 7.565 0.492 6.666 7.545 8.610
beta1_pH[15,2] 6.807 0.387 6.085 6.791 7.593
beta1_pH[16,2] 7.636 0.382 6.890 7.638 8.367
beta1_pH[1,3] 1.946 0.455 1.189 1.918 2.926
beta1_pH[2,3] 0.869 2.479 0.001 0.483 3.888
beta1_pH[3,3] 0.879 2.778 0.000 0.554 3.310
beta1_pH[4,3] 0.997 2.582 0.001 0.534 5.502
beta1_pH[5,3] 5.120 10.156 1.291 2.995 23.131
beta1_pH[6,3] 3.907 4.707 1.257 2.939 13.041
beta1_pH[7,3] 2.834 0.775 1.182 2.818 4.399
beta1_pH[8,3] 2.724 0.316 2.122 2.719 3.350
beta1_pH[9,3] 2.154 0.387 1.385 2.162 2.907
beta1_pH[10,3] 2.605 0.367 1.959 2.585 3.424
beta1_pH[11,4] 2.606 2.135 0.001 2.685 7.072
beta1_pH[12,4] 2.786 2.540 0.001 2.936 5.622
beta1_pH[13,4] 2.889 2.245 0.001 3.352 6.115
beta1_pH[14,4] 2.370 1.914 0.000 2.477 5.350
beta1_pH[15,4] 4.670 9.112 0.001 2.429 43.192
beta1_pH[16,4] 2.577 2.031 0.001 2.574 6.797
beta1_pH[11,5] 6.276 7.878 0.999 3.244 28.084
beta1_pH[12,5] 18.874 18.912 2.848 10.746 68.802
beta1_pH[13,5] 12.554 18.749 0.154 6.099 60.194
beta1_pH[14,5] 25.281 30.014 0.842 11.072 109.827
beta1_pH[15,5] 22.606 115.634 0.210 3.588 121.939
beta1_pH[16,5] 14.060 27.200 0.019 5.528 91.112
beta2_pH[1,1] 0.490 0.163 0.265 0.460 0.882
beta2_pH[2,1] 0.476 0.273 0.172 0.420 1.133
beta2_pH[3,1] 0.455 0.339 0.165 0.389 1.091
beta2_pH[4,1] 0.388 0.173 0.172 0.353 0.802
beta2_pH[5,1] 1.346 1.400 0.097 0.757 5.189
beta2_pH[6,1] 0.818 1.385 0.119 0.328 5.275
beta2_pH[7,1] -0.682 1.586 -4.986 -0.046 0.966
beta2_pH[8,1] 0.408 0.386 0.151 0.330 1.122
beta2_pH[9,1] 0.695 0.706 0.217 0.532 2.477
beta2_pH[10,1] 0.836 0.791 0.261 0.620 2.831
beta2_pH[11,1] 0.239 0.044 0.161 0.236 0.332
beta2_pH[12,1] 1.072 0.589 0.443 0.930 2.644
beta2_pH[13,1] 0.253 0.069 0.140 0.246 0.404
beta2_pH[14,1] 0.247 0.042 0.177 0.242 0.339
beta2_pH[15,1] 0.186 0.056 0.118 0.173 0.320
beta2_pH[16,1] 0.332 0.323 0.110 0.167 1.163
beta2_pH[1,2] -1.161 4.108 -9.306 -1.129 6.873
beta2_pH[2,2] -3.312 3.142 -10.235 -2.963 2.460
beta2_pH[3,2] -3.789 2.577 -9.911 -3.206 -0.625
beta2_pH[4,2] -3.577 3.049 -10.038 -3.256 1.987
beta2_pH[5,2] -1.814 4.099 -10.088 -2.067 6.483
beta2_pH[6,2] -2.588 3.928 -10.218 -2.650 6.120
beta2_pH[7,2] -2.454 3.901 -9.786 -2.635 5.998
beta2_pH[8,2] -2.230 4.181 -10.249 -2.498 6.721
beta2_pH[9,2] -2.517 3.997 -10.143 -2.744 6.853
beta2_pH[10,2] -2.756 3.980 -10.427 -3.009 6.428
beta2_pH[11,2] -6.681 2.583 -13.106 -6.150 -3.104
beta2_pH[12,2] -2.504 2.368 -8.834 -1.425 -0.545
beta2_pH[13,2] -3.254 1.978 -8.675 -2.587 -1.272
beta2_pH[14,2] -4.524 2.226 -10.213 -3.958 -1.771
beta2_pH[15,2] -6.520 2.495 -12.819 -5.986 -3.234
beta2_pH[16,2] -6.788 2.450 -12.854 -6.279 -3.459
beta2_pH[1,3] 4.040 2.479 0.365 3.782 8.811
beta2_pH[2,3] 2.403 3.741 -5.566 2.382 9.567
beta2_pH[3,3] 1.847 4.433 -6.898 2.058 10.651
beta2_pH[4,3] 2.172 3.663 -5.267 2.123 9.555
beta2_pH[5,3] 4.859 2.962 -0.016 4.643 11.348
beta2_pH[6,3] 4.322 3.056 -1.791 4.359 11.100
beta2_pH[7,3] 4.781 2.781 0.597 4.503 11.173
beta2_pH[8,3] 6.281 2.730 2.348 5.805 12.701
beta2_pH[9,3] 5.528 3.006 1.216 5.006 12.899
beta2_pH[10,3] 4.620 2.685 0.619 4.400 10.388
beta2_pH[11,4] -1.336 2.709 -6.619 -0.805 4.384
beta2_pH[12,4] -1.712 2.804 -7.589 -1.232 4.377
beta2_pH[13,4] -1.769 2.959 -8.499 -1.426 4.287
beta2_pH[14,4] -1.080 2.097 -5.330 -1.031 3.398
beta2_pH[15,4] -0.880 3.079 -8.030 -0.533 4.164
beta2_pH[16,4] -0.348 3.688 -8.016 0.151 6.862
beta2_pH[11,5] -3.218 2.763 -11.601 -2.336 -0.416
beta2_pH[12,5] -3.232 1.870 -8.100 -2.977 -0.658
beta2_pH[13,5] -0.298 3.437 -7.686 0.623 6.126
beta2_pH[14,5] -3.961 2.548 -11.404 -3.319 -0.841
beta2_pH[15,5] -1.242 4.061 -9.127 -2.266 4.644
beta2_pH[16,5] -2.125 3.237 -8.800 -2.124 5.364
beta3_pH[1,1] 35.760 1.114 33.737 35.700 38.017
beta3_pH[2,1] 34.523 2.077 31.332 34.223 39.397
beta3_pH[3,1] 35.528 1.785 32.462 35.349 39.558
beta3_pH[4,1] 36.084 1.959 32.764 35.927 40.531
beta3_pH[5,1] 29.127 3.182 25.849 28.039 37.897
beta3_pH[6,1] 40.118 3.796 31.542 41.285 45.242
beta3_pH[7,1] 27.462 8.524 18.464 23.757 45.599
beta3_pH[8,1] 38.581 2.140 34.313 38.726 42.853
beta3_pH[9,1] 30.897 1.807 27.527 30.892 34.550
beta3_pH[10,1] 33.030 1.233 30.776 32.954 35.718
beta3_pH[11,1] 35.461 1.418 33.075 35.381 38.508
beta3_pH[12,1] 30.416 0.578 29.194 30.438 31.437
beta3_pH[13,1] 39.096 2.447 35.305 38.713 44.895
beta3_pH[14,1] 41.459 1.945 38.272 41.169 45.613
beta3_pH[15,1] 41.671 2.686 36.599 41.780 45.832
beta3_pH[16,1] 44.053 1.550 40.424 44.496 45.924
beta3_pH[1,2] 32.236 8.926 18.563 30.660 44.369
beta3_pH[2,2] 29.025 6.408 18.736 28.492 43.814
beta3_pH[3,2] 41.822 0.996 39.962 41.855 43.953
beta3_pH[4,2] 31.462 9.288 18.571 28.152 45.086
beta3_pH[5,2] 30.639 7.995 18.563 30.047 45.063
beta3_pH[6,2] 33.046 6.215 18.996 35.034 44.179
beta3_pH[7,2] 29.922 7.533 18.465 29.534 44.875
beta3_pH[8,2] 29.094 7.509 18.367 27.954 44.409
beta3_pH[9,2] 36.072 9.547 18.615 41.742 45.670
beta3_pH[10,2] 29.786 6.589 18.687 29.612 43.014
beta3_pH[11,2] 43.344 0.140 43.119 43.331 43.648
beta3_pH[12,2] 43.091 0.276 42.461 43.116 43.606
beta3_pH[13,2] 43.831 0.145 43.526 43.845 44.100
beta3_pH[14,2] 43.312 0.154 43.069 43.292 43.650
beta3_pH[15,2] 43.385 0.148 43.135 43.372 43.712
beta3_pH[16,2] 43.482 0.160 43.190 43.477 43.798
beta3_pH[1,3] 40.009 0.864 37.926 40.071 41.268
beta3_pH[2,3] 31.592 7.291 18.749 32.678 44.877
beta3_pH[3,3] 31.291 7.261 18.601 32.025 43.972
beta3_pH[4,3] 27.422 6.978 18.373 26.179 44.063
beta3_pH[5,3] 26.974 6.279 18.372 26.436 42.169
beta3_pH[6,3] 30.823 4.682 19.583 31.721 41.497
beta3_pH[7,3] 25.497 2.055 22.694 24.913 29.561
beta3_pH[8,3] 41.498 0.223 41.084 41.497 41.914
beta3_pH[9,3] 33.776 0.452 32.991 33.784 34.734
beta3_pH[10,3] 36.057 0.519 34.617 36.108 36.864
beta3_pH[11,4] 40.520 5.056 29.587 42.928 45.827
beta3_pH[12,4] 40.688 3.641 30.050 42.143 44.889
beta3_pH[13,4] 40.969 4.248 30.070 42.925 45.496
beta3_pH[14,4] 40.671 4.124 30.043 42.099 45.557
beta3_pH[15,4] 36.910 6.509 29.385 32.834 45.815
beta3_pH[16,4] 36.977 6.602 29.170 35.353 45.822
beta3_pH[11,5] 40.068 1.783 35.564 40.151 42.721
beta3_pH[12,5] 38.118 1.895 34.638 38.021 42.546
beta3_pH[13,5] 36.644 4.295 30.529 35.585 44.387
beta3_pH[14,5] 39.322 1.543 36.117 39.331 42.550
beta3_pH[15,5] 36.862 4.796 29.126 39.867 41.072
beta3_pH[16,5] 37.869 3.200 29.986 38.544 44.393
beta0_pelagic[1] 1.906 0.457 0.611 2.071 2.396
beta0_pelagic[2] 1.375 0.321 0.402 1.458 1.724
beta0_pelagic[3] 0.251 0.343 -0.678 0.322 0.731
beta0_pelagic[4] 0.333 0.391 -0.501 0.362 1.051
beta0_pelagic[5] -0.299 1.599 -3.242 -0.295 1.618
beta0_pelagic[6] 1.481 0.344 0.413 1.555 1.833
beta0_pelagic[7] 1.529 0.136 1.248 1.529 1.786
beta0_pelagic[8] 1.846 0.143 1.550 1.848 2.114
beta0_pelagic[9] 1.761 0.869 -0.595 1.893 2.811
beta0_pelagic[10] 2.551 0.192 2.019 2.573 2.820
beta0_pelagic[11] 0.695 0.127 0.442 0.697 0.921
beta0_pelagic[12] 1.756 0.130 1.502 1.756 2.010
beta0_pelagic[13] 0.559 0.160 0.261 0.551 0.883
beta0_pelagic[14] 0.376 0.203 -0.078 0.392 0.708
beta0_pelagic[15] -0.266 0.124 -0.512 -0.265 -0.025
beta0_pelagic[16] 0.570 0.128 0.318 0.571 0.815
beta1_pelagic[1] 0.339 0.456 0.000 0.110 1.635
beta1_pelagic[2] 0.214 0.329 0.000 0.058 1.148
beta1_pelagic[3] 0.847 0.482 0.219 0.732 2.273
beta1_pelagic[4] 0.849 0.418 0.001 0.833 1.678
beta1_pelagic[5] 1.819 1.719 0.000 1.925 4.896
beta1_pelagic[6] 0.388 2.889 0.000 0.011 1.864
beta1_pelagic[7] 4.461 5.965 0.000 0.263 18.388
beta1_pelagic[8] 0.254 0.745 0.000 0.010 1.939
beta1_pelagic[9] 1.131 0.968 0.000 1.039 3.637
beta1_pelagic[10] 0.241 0.825 0.000 0.008 2.632
beta1_pelagic[11] 2.370 0.236 1.899 2.380 2.813
beta1_pelagic[12] 2.627 0.263 2.120 2.620 3.158
beta1_pelagic[13] 2.354 0.473 1.622 2.293 3.462
beta1_pelagic[14] 3.245 0.715 2.208 3.103 5.089
beta1_pelagic[15] 2.529 0.232 2.121 2.517 2.982
beta1_pelagic[16] 2.989 0.245 2.503 2.988 3.481
beta2_pelagic[1] 2.008 2.981 -4.441 1.818 8.872
beta2_pelagic[2] 2.211 3.049 -4.004 1.881 9.197
beta2_pelagic[3] 2.017 2.206 0.090 1.432 8.252
beta2_pelagic[4] 2.714 2.181 0.137 2.416 8.304
beta2_pelagic[5] -1.646 3.599 -8.310 -2.196 6.538
beta2_pelagic[6] 0.807 3.717 -7.207 0.828 7.980
beta2_pelagic[7] -1.803 4.224 -9.677 -2.247 6.832
beta2_pelagic[8] -0.239 3.854 -7.892 -0.482 7.558
beta2_pelagic[9] 2.407 2.552 -2.922 2.101 6.314
beta2_pelagic[10] -0.222 4.288 -8.533 -0.273 8.573
beta2_pelagic[11] 4.573 2.702 1.211 3.954 11.267
beta2_pelagic[12] 5.764 2.722 1.773 5.273 12.236
beta2_pelagic[13] 1.823 2.322 0.308 0.872 9.137
beta2_pelagic[14] 0.519 0.472 0.201 0.438 1.208
beta2_pelagic[15] 5.915 2.699 2.028 5.504 12.695
beta2_pelagic[16] 5.861 2.978 1.293 5.424 13.203
beta3_pelagic[1] 27.056 7.561 18.377 23.901 44.715
beta3_pelagic[2] 28.295 8.328 18.345 25.297 45.275
beta3_pelagic[3] 29.842 4.525 22.219 29.798 40.937
beta3_pelagic[4] 25.367 2.870 20.875 25.296 33.313
beta3_pelagic[5] 38.909 9.504 18.866 45.390 45.994
beta3_pelagic[6] 29.740 7.933 18.442 28.446 44.693
beta3_pelagic[7] 25.361 7.900 18.512 20.565 44.208
beta3_pelagic[8] 29.176 7.651 18.441 27.640 44.781
beta3_pelagic[9] 28.433 5.582 19.474 26.662 41.865
beta3_pelagic[10] 29.263 8.368 18.325 27.814 44.817
beta3_pelagic[11] 43.217 0.347 42.355 43.233 43.814
beta3_pelagic[12] 43.461 0.239 43.045 43.457 43.907
beta3_pelagic[13] 42.985 0.897 41.269 42.966 44.922
beta3_pelagic[14] 43.001 1.277 40.584 42.964 45.620
beta3_pelagic[15] 43.219 0.204 42.817 43.202 43.640
beta3_pelagic[16] 43.280 0.225 42.804 43.273 43.713
mu_beta0_pelagic[1] 0.922 0.776 -0.680 0.942 2.442
mu_beta0_pelagic[2] 1.429 0.767 -0.348 1.577 2.639
mu_beta0_pelagic[3] 0.596 0.410 -0.269 0.605 1.385
tau_beta0_pelagic[1] 1.617 4.712 0.071 0.716 8.195
tau_beta0_pelagic[2] 1.819 3.473 0.071 0.716 8.412
tau_beta0_pelagic[3] 1.815 1.361 0.231 1.466 5.360
beta0_yellow[1] -0.525 0.178 -0.927 -0.507 -0.223
beta0_yellow[2] 0.438 0.300 -0.210 0.485 0.764
beta0_yellow[3] -0.310 0.173 -0.681 -0.303 0.006
beta0_yellow[4] 0.744 0.362 -0.290 0.841 1.190
beta0_yellow[5] -1.208 0.419 -2.059 -1.207 -0.425
beta0_yellow[6] 0.236 0.207 -0.178 0.240 0.636
beta0_yellow[7] 0.389 0.891 -1.504 0.893 1.315
beta0_yellow[8] 0.512 0.782 -1.442 0.868 1.261
beta0_yellow[9] -0.062 0.275 -0.568 -0.073 0.512
beta0_yellow[10] 0.237 0.149 -0.059 0.236 0.547
beta0_yellow[11] -1.430 0.950 -2.858 -1.744 0.030
beta0_yellow[12] -3.631 0.449 -4.592 -3.603 -2.810
beta0_yellow[13] -3.621 0.486 -4.608 -3.585 -2.754
beta0_yellow[14] -1.701 0.878 -2.898 -1.976 0.054
beta0_yellow[15] -2.878 0.417 -3.793 -2.851 -2.149
beta0_yellow[16] -2.358 0.501 -3.389 -2.366 -1.378
beta1_yellow[1] 0.476 0.597 0.000 0.326 1.868
beta1_yellow[2] 1.185 0.716 0.594 1.042 3.714
beta1_yellow[3] 0.662 0.258 0.131 0.661 1.164
beta1_yellow[4] 1.610 0.995 0.651 1.261 4.478
beta1_yellow[5] 2.841 1.009 1.284 2.714 5.309
beta1_yellow[6] 2.297 0.325 1.670 2.298 2.965
beta1_yellow[7] 3.601 3.419 0.313 2.434 13.737
beta1_yellow[8] 2.052 1.773 0.058 1.775 6.356
beta1_yellow[9] 1.585 0.836 0.809 1.547 2.402
beta1_yellow[10] 2.584 0.468 1.740 2.554 3.576
beta1_yellow[11] 2.151 0.930 0.621 2.175 3.907
beta1_yellow[12] 2.430 0.460 1.593 2.407 3.368
beta1_yellow[13] 2.826 0.488 1.983 2.795 3.825
beta1_yellow[14] 2.203 1.071 0.477 2.174 5.140
beta1_yellow[15] 2.183 0.438 1.396 2.157 3.073
beta1_yellow[16] 2.178 0.507 1.165 2.185 3.232
beta2_yellow[1] -2.851 3.124 -10.244 -2.175 2.168
beta2_yellow[2] -3.128 2.772 -10.129 -2.336 -0.082
beta2_yellow[3] -3.156 2.780 -10.189 -2.417 -0.148
beta2_yellow[4] -2.859 3.214 -11.046 -1.583 -0.079
beta2_yellow[5] -4.364 2.788 -11.119 -3.866 -0.587
beta2_yellow[6] 3.653 2.147 0.974 3.162 9.070
beta2_yellow[7] -1.513 4.955 -10.844 -2.028 7.951
beta2_yellow[8] -1.217 4.446 -10.473 -1.159 8.058
beta2_yellow[9] 3.947 2.677 0.222 3.618 9.773
beta2_yellow[10] -5.809 2.821 -10.988 -6.060 -1.100
beta2_yellow[11] -2.702 2.018 -7.753 -2.233 -0.332
beta2_yellow[12] -3.321 1.750 -7.759 -3.008 -0.932
beta2_yellow[13] -3.396 1.810 -7.942 -2.980 -1.223
beta2_yellow[14] -3.118 2.132 -8.621 -2.746 -0.138
beta2_yellow[15] -3.061 1.744 -7.702 -2.729 -0.883
beta2_yellow[16] -3.404 1.902 -8.102 -2.994 -1.110
beta3_yellow[1] 27.529 7.127 18.444 25.897 43.874
beta3_yellow[2] 29.013 2.061 23.475 28.900 32.927
beta3_yellow[3] 32.860 3.104 25.011 32.852 39.427
beta3_yellow[4] 29.062 3.850 20.266 28.155 36.269
beta3_yellow[5] 33.398 1.482 30.773 33.446 35.755
beta3_yellow[6] 39.636 0.514 38.755 39.591 40.822
beta3_yellow[7] 22.839 4.449 18.562 20.586 35.200
beta3_yellow[8] 25.568 5.644 18.352 24.782 42.256
beta3_yellow[9] 37.604 2.376 36.067 37.595 42.514
beta3_yellow[10] 29.393 0.423 28.389 29.445 29.984
beta3_yellow[11] 40.535 7.135 26.881 45.185 45.972
beta3_yellow[12] 43.436 0.484 42.557 43.403 44.543
beta3_yellow[13] 44.765 0.414 43.906 44.820 45.485
beta3_yellow[14] 41.033 6.835 21.509 44.085 45.843
beta3_yellow[15] 45.342 0.474 44.271 45.397 45.975
beta3_yellow[16] 44.668 0.628 43.507 44.663 45.865
mu_beta0_yellow[1] 0.088 0.563 -1.118 0.096 1.233
mu_beta0_yellow[2] 0.007 0.498 -0.983 0.018 0.981
mu_beta0_yellow[3] -2.200 0.765 -3.361 -2.337 -0.341
tau_beta0_yellow[1] 2.113 3.250 0.100 1.209 8.919
tau_beta0_yellow[2] 1.720 2.574 0.161 1.103 6.531
tau_beta0_yellow[3] 1.386 2.545 0.072 0.672 6.667
beta0_black[1] 0.000 0.195 -0.360 -0.011 0.383
beta0_black[2] 1.863 0.204 1.444 1.886 2.132
beta0_black[3] 1.284 0.157 0.948 1.296 1.549
beta0_black[4] 2.134 0.411 1.593 2.162 2.598
beta0_black[5] 1.589 1.997 -2.941 1.647 5.689
beta0_black[6] 1.568 1.945 -3.008 1.646 5.437
beta0_black[7] 1.533 1.871 -2.695 1.621 5.528
beta0_black[8] 1.237 0.240 0.734 1.245 1.680
beta0_black[9] 2.397 0.278 1.817 2.409 2.872
beta0_black[10] 1.455 0.139 1.188 1.458 1.706
beta0_black[11] 3.332 0.405 2.382 3.403 3.734
beta0_black[12] 4.475 0.191 4.102 4.479 4.833
beta0_black[13] -0.100 0.220 -0.550 -0.096 0.332
beta0_black[14] 1.977 1.050 -1.197 2.238 2.752
beta0_black[15] 1.129 0.321 0.176 1.194 1.524
beta0_black[16] 4.114 0.466 2.572 4.228 4.550
beta2_black[1] 2.406 3.542 -5.923 2.509 9.304
beta2_black[2] 1.550 3.154 -5.994 1.850 6.651
beta2_black[3] -0.556 3.750 -7.002 -0.763 7.182
beta2_black[4] -1.764 3.372 -8.351 -1.596 6.031
beta2_black[5] -1.127 4.240 -9.091 -1.341 7.813
beta2_black[6] -1.142 4.218 -8.887 -1.225 7.667
beta2_black[7] -1.132 4.208 -9.037 -1.394 7.672
beta2_black[8] -1.278 4.252 -9.301 -1.556 7.639
beta2_black[9] -1.124 4.198 -9.153 -1.403 7.698
beta2_black[10] -1.625 3.955 -8.216 -2.024 7.303
beta2_black[11] -1.725 1.719 -4.682 -1.326 0.521
beta2_black[12] -2.762 1.681 -7.072 -2.381 -0.662
beta2_black[13] -2.357 1.804 -7.280 -1.831 -0.507
beta2_black[14] -1.742 1.878 -6.721 -1.092 -0.044
beta2_black[15] -2.030 2.308 -7.455 -1.627 1.935
beta2_black[16] -1.898 2.181 -6.028 -1.776 2.310
beta3_black[1] 37.854 7.373 19.212 41.517 43.550
beta3_black[2] 30.038 8.317 18.388 28.991 45.099
beta3_black[3] 29.683 8.030 18.400 28.742 45.059
beta3_black[4] 32.219 5.440 19.298 32.847 42.833
beta3_black[5] 30.313 7.965 18.582 29.426 45.021
beta3_black[6] 30.172 7.878 18.498 29.415 44.737
beta3_black[7] 29.907 7.875 18.473 28.680 44.659
beta3_black[8] 30.174 8.162 18.407 29.419 44.865
beta3_black[9] 30.398 8.074 18.478 29.613 44.897
beta3_black[10] 29.304 7.918 18.459 28.058 44.856
beta3_black[11] 29.953 6.912 18.601 29.839 43.906
beta3_black[12] 32.925 1.166 31.114 32.959 34.015
beta3_black[13] 39.315 0.651 37.841 39.379 40.463
beta3_black[14] 38.051 3.926 26.982 38.826 44.875
beta3_black[15] 31.623 7.859 18.620 31.393 45.053
beta3_black[16] 27.797 7.504 18.334 26.092 44.805
beta4_black[1] -0.259 0.185 -0.625 -0.259 0.087
beta4_black[2] 0.249 0.171 -0.090 0.245 0.581
beta4_black[3] -0.933 0.180 -1.282 -0.928 -0.584
beta4_black[4] 0.495 0.226 0.060 0.487 0.938
beta4_black[5] 0.249 2.574 -4.614 0.178 5.334
beta4_black[6] 0.166 2.715 -4.715 0.130 5.231
beta4_black[7] 0.257 2.388 -4.158 0.168 4.980
beta4_black[8] -0.682 0.357 -1.384 -0.684 0.029
beta4_black[9] 1.489 1.013 -0.098 1.362 3.785
beta4_black[10] 0.023 0.181 -0.326 0.021 0.390
beta4_black[11] -0.690 0.212 -1.109 -0.689 -0.261
beta4_black[12] 0.291 0.325 -0.330 0.285 0.961
beta4_black[13] -1.195 0.212 -1.608 -1.194 -0.782
beta4_black[14] -0.128 0.231 -0.568 -0.131 0.339
beta4_black[15] -0.891 0.203 -1.295 -0.891 -0.504
beta4_black[16] -0.599 0.223 -1.033 -0.602 -0.163
mu_beta0_black[1] 1.239 0.869 -0.667 1.264 2.943
mu_beta0_black[2] 1.556 0.915 -0.683 1.616 3.247
mu_beta0_black[3] 2.219 1.000 -0.015 2.271 4.068
tau_beta0_black[1] 0.752 0.723 0.061 0.529 2.647
tau_beta0_black[2] 2.090 4.932 0.056 0.804 10.875
tau_beta0_black[3] 0.254 0.179 0.051 0.210 0.724
beta0_dsr[11] -3.050 0.275 -3.579 -3.059 -2.501
beta0_dsr[12] 4.459 0.274 3.930 4.455 4.990
beta0_dsr[13] -2.065 1.106 -6.128 -1.697 -1.075
beta0_dsr[14] -4.241 0.473 -5.173 -4.233 -3.340
beta0_dsr[15] -2.393 0.256 -2.887 -2.390 -1.884
beta0_dsr[16] -3.082 0.350 -3.765 -3.090 -2.390
beta1_dsr[11] 4.929 0.291 4.334 4.934 5.506
beta1_dsr[12] 6.131 3.533 2.520 5.362 14.109
beta1_dsr[13] 3.697 1.341 2.529 3.178 8.166
beta1_dsr[14] 6.878 0.504 5.902 6.867 7.865
beta1_dsr[15] 3.587 0.262 3.049 3.594 4.085
beta1_dsr[16] 5.875 0.366 5.153 5.878 6.565
beta2_dsr[11] -8.176 2.288 -13.506 -7.937 -4.562
beta2_dsr[12] -6.813 2.552 -12.377 -6.665 -2.374
beta2_dsr[13] -3.775 3.113 -9.657 -2.849 -0.200
beta2_dsr[14] -5.966 2.250 -10.918 -5.726 -2.325
beta2_dsr[15] -7.780 1.995 -11.412 -7.742 -4.129
beta2_dsr[16] -7.883 2.273 -13.191 -7.627 -4.244
beta3_dsr[11] 43.487 0.148 43.218 43.481 43.768
beta3_dsr[12] 34.060 0.601 32.536 34.184 34.813
beta3_dsr[13] 43.461 0.997 42.255 43.220 46.926
beta3_dsr[14] 43.283 0.138 43.090 43.258 43.617
beta3_dsr[15] 43.469 0.185 43.146 43.462 43.815
beta3_dsr[16] 43.434 0.155 43.177 43.420 43.746
beta4_dsr[11] 0.662 0.211 0.260 0.665 1.085
beta4_dsr[12] 0.315 0.466 -0.590 0.307 1.272
beta4_dsr[13] -0.098 0.208 -0.514 -0.090 0.299
beta4_dsr[14] 0.195 0.246 -0.287 0.197 0.675
beta4_dsr[15] 0.978 0.213 0.566 0.981 1.398
beta4_dsr[16] 0.171 0.220 -0.244 0.174 0.590
beta0_slope[11] -2.006 0.156 -2.312 -2.007 -1.704
beta0_slope[12] -4.662 0.256 -5.186 -4.656 -4.174
beta0_slope[13] -1.441 0.229 -2.008 -1.418 -1.085
beta0_slope[14] -2.764 0.180 -3.122 -2.764 -2.408
beta0_slope[15] -1.712 0.157 -2.017 -1.710 -1.409
beta0_slope[16] -2.758 0.168 -3.074 -2.760 -2.430
beta1_slope[11] 4.386 0.288 3.829 4.389 4.958
beta1_slope[12] 4.842 0.547 3.801 4.834 5.919
beta1_slope[13] 2.733 0.537 2.017 2.636 4.275
beta1_slope[14] 5.237 0.596 4.213 5.192 6.497
beta1_slope[15] 2.045 0.266 1.529 2.044 2.568
beta1_slope[16] 5.287 0.400 4.513 5.278 6.097
beta2_slope[11] 7.238 2.306 3.635 6.913 12.483
beta2_slope[12] 5.443 2.471 1.707 5.063 11.413
beta2_slope[13] 3.563 2.355 0.317 3.123 9.273
beta2_slope[14] 1.589 0.631 0.869 1.413 3.269
beta2_slope[15] 5.013 2.515 2.277 4.527 10.982
beta2_slope[16] 6.190 2.167 3.026 5.819 11.498
beta3_slope[11] 43.524 0.132 43.268 43.526 43.780
beta3_slope[12] 43.486 0.191 43.106 43.490 43.847
beta3_slope[13] 43.590 0.258 43.094 43.585 44.057
beta3_slope[14] 43.845 0.357 43.359 43.765 44.769
beta3_slope[15] 43.586 0.191 43.236 43.573 43.989
beta3_slope[16] 43.515 0.142 43.246 43.511 43.793
beta4_slope[11] -0.453 0.208 -0.857 -0.450 -0.057
beta4_slope[12] -1.214 0.675 -2.787 -1.114 -0.166
beta4_slope[13] 0.180 0.206 -0.210 0.177 0.598
beta4_slope[14] -0.060 0.243 -0.511 -0.070 0.430
beta4_slope[15] -0.193 0.202 -0.592 -0.194 0.202
beta4_slope[16] -0.130 0.224 -0.573 -0.130 0.305
sigma_H[1] 0.197 0.051 0.101 0.194 0.304
sigma_H[2] 0.172 0.030 0.120 0.170 0.237
sigma_H[3] 0.197 0.042 0.125 0.194 0.286
sigma_H[4] 0.421 0.077 0.290 0.414 0.590
sigma_H[5] 0.983 0.206 0.598 0.976 1.431
sigma_H[6] 0.376 0.201 0.029 0.367 0.799
sigma_H[7] 0.297 0.058 0.205 0.291 0.427
sigma_H[8] 0.425 0.098 0.267 0.413 0.632
sigma_H[9] 0.515 0.118 0.328 0.500 0.787
sigma_H[10] 0.218 0.044 0.142 0.214 0.313
sigma_H[11] 0.278 0.046 0.201 0.274 0.380
sigma_H[12] 0.446 0.165 0.208 0.429 0.781
sigma_H[13] 0.215 0.038 0.148 0.212 0.299
sigma_H[14] 0.508 0.091 0.348 0.503 0.698
sigma_H[15] 0.251 0.042 0.183 0.248 0.343
sigma_H[16] 0.222 0.043 0.150 0.217 0.321
lambda_H[1] 3.024 3.995 0.154 1.676 14.047
lambda_H[2] 8.347 7.703 0.763 6.161 28.120
lambda_H[3] 6.181 9.604 0.258 3.064 31.887
lambda_H[4] 0.006 0.004 0.001 0.005 0.017
lambda_H[5] 4.082 9.582 0.032 1.001 31.760
lambda_H[6] 7.959 15.522 0.008 1.046 52.551
lambda_H[7] 0.015 0.010 0.002 0.012 0.041
lambda_H[8] 8.056 10.269 0.072 4.570 37.003
lambda_H[9] 0.015 0.010 0.003 0.013 0.042
lambda_H[10] 0.385 1.839 0.033 0.196 1.251
lambda_H[11] 0.248 0.376 0.011 0.131 1.210
lambda_H[12] 4.815 6.230 0.213 2.721 21.475
lambda_H[13] 3.169 2.781 0.225 2.398 10.614
lambda_H[14] 3.586 5.025 0.220 2.148 14.892
lambda_H[15] 0.038 0.505 0.004 0.017 0.119
lambda_H[16] 0.992 1.335 0.047 0.511 4.645
mu_lambda_H[1] 4.325 1.874 1.247 4.115 8.348
mu_lambda_H[2] 3.871 1.966 0.660 3.736 8.088
mu_lambda_H[3] 3.431 1.814 0.726 3.158 7.614
sigma_lambda_H[1] 8.627 4.272 1.963 7.947 18.081
sigma_lambda_H[2] 8.474 4.716 1.119 7.899 18.275
sigma_lambda_H[3] 6.102 3.904 0.980 5.297 15.924
beta_H[1,1] 6.882 1.064 4.337 7.052 8.564
beta_H[2,1] 9.882 0.488 8.824 9.910 10.794
beta_H[3,1] 8.005 0.787 6.093 8.105 9.300
beta_H[4,1] 9.444 7.786 -6.224 9.456 24.819
beta_H[5,1] 0.104 2.364 -4.924 0.299 3.930
beta_H[6,1] 3.155 3.986 -7.153 4.651 7.531
beta_H[7,1] 1.381 5.495 -10.668 1.815 10.764
beta_H[8,1] 1.619 4.976 -2.267 1.243 3.917
beta_H[9,1] 12.967 5.758 1.527 12.956 24.815
beta_H[10,1] 7.117 1.704 3.610 7.137 10.567
beta_H[11,1] 5.245 3.446 -2.662 6.017 10.040
beta_H[12,1] 2.620 1.045 0.740 2.572 4.837
beta_H[13,1] 9.037 0.993 7.084 9.121 10.555
beta_H[14,1] 2.170 0.996 0.193 2.181 4.180
beta_H[15,1] -5.870 4.057 -13.099 -6.272 3.110
beta_H[16,1] 3.290 2.535 -0.745 2.992 9.212
beta_H[1,2] 7.897 0.245 7.400 7.902 8.363
beta_H[2,2] 10.024 0.133 9.756 10.023 10.286
beta_H[3,2] 8.961 0.199 8.587 8.959 9.348
beta_H[4,2] 3.553 1.500 0.682 3.531 6.512
beta_H[5,2] 1.960 0.958 0.099 1.969 3.821
beta_H[6,2] 5.765 1.090 3.150 5.952 7.446
beta_H[7,2] 2.365 1.092 0.428 2.293 4.671
beta_H[8,2] 2.934 1.346 1.018 3.143 4.280
beta_H[9,2] 3.449 1.117 1.366 3.421 5.713
beta_H[10,2] 8.180 0.355 7.447 8.192 8.853
beta_H[11,2] 9.716 0.614 8.794 9.593 11.140
beta_H[12,2] 3.961 0.378 3.263 3.940 4.733
beta_H[13,2] 9.114 0.261 8.645 9.102 9.641
beta_H[14,2] 4.001 0.338 3.353 3.994 4.671
beta_H[15,2] 11.323 0.727 9.762 11.374 12.631
beta_H[16,2] 4.493 0.790 3.025 4.499 6.011
beta_H[1,3] 8.487 0.241 8.036 8.474 9.002
beta_H[2,3] 10.076 0.114 9.854 10.073 10.305
beta_H[3,3] 9.615 0.168 9.297 9.611 9.961
beta_H[4,3] -2.484 0.904 -4.257 -2.489 -0.718
beta_H[5,3] 3.870 0.628 2.608 3.871 5.091
beta_H[6,3] 8.114 1.235 6.413 7.720 10.747
beta_H[7,3] -2.429 0.749 -3.960 -2.424 -1.004
beta_H[8,3] 5.288 0.621 4.652 5.192 6.557
beta_H[9,3] -2.751 0.720 -4.182 -2.736 -1.386
beta_H[10,3] 8.745 0.278 8.200 8.740 9.310
beta_H[11,3] 8.544 0.279 7.942 8.570 9.029
beta_H[12,3] 5.253 0.325 4.506 5.293 5.788
beta_H[13,3] 8.822 0.182 8.461 8.827 9.172
beta_H[14,3] 5.678 0.276 5.090 5.699 6.180
beta_H[15,3] 10.373 0.334 9.733 10.369 11.051
beta_H[16,3] 6.231 0.667 4.793 6.308 7.330
beta_H[1,4] 8.271 0.178 7.894 8.282 8.588
beta_H[2,4] 10.137 0.120 9.878 10.146 10.350
beta_H[3,4] 10.117 0.162 9.773 10.127 10.399
beta_H[4,4] 11.772 0.458 10.837 11.777 12.632
beta_H[5,4] 5.511 0.743 4.315 5.412 7.225
beta_H[6,4] 7.112 0.939 4.910 7.388 8.384
beta_H[7,4] 8.177 0.343 7.501 8.170 8.833
beta_H[8,4] 6.692 0.283 6.130 6.712 7.140
beta_H[9,4] 7.208 0.466 6.298 7.207 8.124
beta_H[10,4] 7.763 0.246 7.302 7.751 8.263
beta_H[11,4] 9.292 0.205 8.890 9.297 9.679
beta_H[12,4] 7.142 0.213 6.722 7.144 7.562
beta_H[13,4] 9.009 0.145 8.717 9.009 9.290
beta_H[14,4] 7.654 0.213 7.248 7.654 8.066
beta_H[15,4] 9.434 0.245 8.952 9.429 9.932
beta_H[16,4] 9.239 0.237 8.837 9.222 9.735
beta_H[1,5] 8.982 0.142 8.694 8.985 9.254
beta_H[2,5] 10.781 0.093 10.606 10.779 10.972
beta_H[3,5] 10.926 0.175 10.620 10.916 11.291
beta_H[4,5] 8.399 0.465 7.473 8.397 9.359
beta_H[5,5] 5.381 0.597 3.931 5.439 6.372
beta_H[6,5] 8.743 0.616 7.849 8.614 10.253
beta_H[7,5] 6.818 0.334 6.175 6.812 7.504
beta_H[8,5] 8.220 0.239 7.852 8.198 8.706
beta_H[9,5] 8.185 0.473 7.284 8.179 9.113
beta_H[10,5] 10.085 0.234 9.585 10.093 10.530
beta_H[11,5] 11.539 0.234 11.062 11.542 11.999
beta_H[12,5] 8.498 0.199 8.115 8.494 8.896
beta_H[13,5] 10.008 0.132 9.743 10.007 10.263
beta_H[14,5] 9.181 0.233 8.751 9.168 9.672
beta_H[15,5] 11.174 0.250 10.676 11.172 11.662
beta_H[16,5] 9.929 0.171 9.577 9.933 10.256
beta_H[1,6] 10.179 0.187 9.849 10.166 10.575
beta_H[2,6] 11.514 0.107 11.305 11.514 11.731
beta_H[3,6] 10.807 0.166 10.458 10.819 11.100
beta_H[4,6] 12.870 0.816 11.236 12.890 14.447
beta_H[5,6] 5.888 0.599 4.765 5.863 7.095
beta_H[6,6] 8.742 0.679 6.849 8.863 9.724
beta_H[7,6] 9.793 0.550 8.747 9.796 10.862
beta_H[8,6] 9.498 0.311 8.931 9.528 9.965
beta_H[9,6] 8.479 0.796 6.894 8.483 10.104
beta_H[10,6] 9.519 0.316 8.830 9.542 10.070
beta_H[11,6] 10.806 0.355 10.065 10.831 11.464
beta_H[12,6] 9.393 0.254 8.892 9.388 9.925
beta_H[13,6] 11.063 0.170 10.758 11.055 11.433
beta_H[14,6] 9.861 0.287 9.287 9.860 10.422
beta_H[15,6] 10.858 0.437 9.992 10.852 11.727
beta_H[16,6] 10.528 0.236 9.980 10.542 10.951
beta_H[1,7] 10.853 0.871 8.740 10.968 12.311
beta_H[2,7] 12.214 0.428 11.357 12.226 13.062
beta_H[3,7] 10.538 0.683 9.022 10.605 11.686
beta_H[4,7] 2.573 4.171 -5.702 2.477 11.075
beta_H[5,7] 6.468 1.876 3.120 6.374 10.717
beta_H[6,7] 9.578 2.471 4.836 9.465 16.372
beta_H[7,7] 10.790 2.766 5.260 10.829 16.119
beta_H[8,7] 11.008 1.236 9.483 10.888 13.136
beta_H[9,7] 4.462 4.053 -3.598 4.524 12.658
beta_H[10,7] 9.845 1.470 7.254 9.758 13.078
beta_H[11,7] 10.980 1.727 7.857 10.839 14.759
beta_H[12,7] 10.025 0.919 8.002 10.102 11.561
beta_H[13,7] 11.645 0.798 9.843 11.755 12.878
beta_H[14,7] 10.482 0.949 8.462 10.557 12.178
beta_H[15,7] 12.168 2.311 7.662 12.136 16.764
beta_H[16,7] 12.228 1.268 10.198 12.031 15.335
beta0_H[1] 9.040 12.630 -17.085 9.278 34.827
beta0_H[2] 10.547 6.421 -2.533 10.526 23.302
beta0_H[3] 9.513 10.241 -11.681 9.658 30.032
beta0_H[4] 7.390 181.054 -359.229 8.101 362.814
beta0_H[5] 4.220 26.936 -42.981 4.472 52.820
beta0_H[6] 7.013 49.060 -100.642 7.658 109.127
beta0_H[7] 3.488 125.932 -256.656 4.228 258.021
beta0_H[8] 7.069 35.226 -18.688 6.519 32.679
beta0_H[9] 7.659 120.783 -240.029 6.455 258.721
beta0_H[10] 9.325 32.734 -56.281 8.803 76.534
beta0_H[11] 8.971 50.488 -94.972 9.388 113.566
beta0_H[12] 6.647 11.465 -15.676 6.822 27.238
beta0_H[13] 9.606 11.056 -11.822 9.814 29.918
beta0_H[14] 7.123 11.152 -14.497 7.136 28.240
beta0_H[15] 6.813 104.563 -200.400 5.481 229.744
beta0_H[16] 8.195 24.717 -45.118 7.851 62.545